Robust PCA with Lw, and L2,1 Norms: A Novel Method for Low-Quality Retinal Image Enhancement*

Nonmydriatic retinal fundus images often suffer from quality issues and artifacts due to ocular or systemic comorbidities, leading to potential inaccuracies in clinical diagnoses. In recent times, deep learning methods have been widely employed to improve retinal image quality. However, these methods often require large datasets and lack robustness in clinical settings. Conversely, the inherent stability and adaptability of traditional unsupervised learning methods, coupled with their reduced reliance on extensive data, render them more suitable for real-world clinical applications, particularly in the limited data context of high noise levels or a significant presence of artifacts. However, existing unsupervised learning methods encounter challenges such as sensitivity to noise and outliers, reliance on assumptions like cluster shapes, and difficulties with scalability and interpretability, particularly when utilized for retinal image enhancement. To tackle these challenges, we propose a novel robust PCA (RPCA) method with low-rank sparse decomposition that also integrates affine transformations τi, weighted nuclear norm, and the L2,1 norms, aiming to overcome existing method limitations and to achieve image quality improvement unseen by these methods. We employ the weighted nuclear norm (Lw,∗) to assign weights to singular values to each retinal images and utilize the L2,1 norm to eliminate correlated samples and outliers in the retinal images. Moreover, τi is employed to enhance retinal image alignment, making the new method more robust to variations, outliers, noise, and image blurring. The Alternating Direction Method of Multipliers (ADMM) method is used to optimally determine parameters, including τi, by solving an optimization problem. Each parameter is addressed separately, harnessing the benefits of ADMM. Our method introduces a novel parameter update approach and significantly improves retinal image quality, detecting cataracts, and diabetic retinopathy. Simulation results confirm our method's superiority over existing state-of-the-art methods across various datasets.